Publication: Projection methods for large-scale T-Sylvester equations
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2015-05
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American Mathematical Society
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Abstract
The matrix Sylvester equation for congruence, or T-Sylvester equation, has recently attracted considerable attention as a consequence of its close relation to palindromic eigenvalue problems. The theory concerning T-Sylvester equations is rather well understood and there are stable and e cient numerical algorithms which solve these equations for small- to medium-sized matrices. However, developing numerical algorithms for solving large-scale T-Sylvester equations still remains an open problem. In this paper, we present several projection algorithms based on di erent Krylov spaces for solving this problem when the right-hand side of the T-Sylvester equation is a low-rank matrix. The new algorithms have been extensively tested, and the reported numerical results show that they work very well in practice, o ering a clear guidance on which algorithm is the most convenient in each situation.
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matrix equations, Krylov subspace, iterative methods, large-scale equations, Sylvester equation, Sylvester equation for congruence.
Bibliographic citation
Mathematics of Computation (2015) 5